While shopping at a music store, Rick bought 7 CD’s, all at the same price. The tax was $6.50 and the total was $66.00. What was the price of each CD?

Answer:

3.4051451e+12

Step-by-step explanation:

:/

Answer:

3.40515e12

Step-by-step explanation:

Answer:

\(y = \frac{1}{8} x - 2 \frac{1}{4} \)

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept

Line p: y= -8x +6

slope= -8

The product of the slopes of perpendicular lines is -1. Let the slope of line q be m.

m(-8)= -1

m= -1 ÷(-8)

m= ⅛

Substitute m= ⅛ into the equation:

y= ⅛x +c

To find the value of c, substitute a pair of coordinates that the line passes through into the equation.

When x= 2, y= -2,

-2= ⅛(2) +c

\( - 2 = \frac{1}{4} + c\)

\(c = - 2 - \frac{1}{4} \)

\(c = - 2 \frac{1}{4} \)

Thus, the equation of line q is \(y = \frac{1}{8} x - 2 \frac{1}{4} \).

Answer:

y=1/8x-9/4

Step-by-step explanation:

Answer:

length = 62.41 inches

Step-by-step explanation:

Using pythagoras theorem -

Let

a = hypotenuse

b = height

c = length

a^2 = b^2 +c^2

75^2 = 41.6^2 + c^2

Therefore,

75^2 - 41.6^2 = c^2

5625 - 1730.56 = c^2

389.44 = c^2

square root (389.44) = c

62.40544848 = c

Answer:

62 inches.

Step-by-step explanation:

and finally, take the square root of the number we are left with after subtracting \(B^{2}\) , or 1730.56, from 5625, or \(C^{2}\)

5625 - 1730.56 =3894.44

\(\sqrt{3894.44}\) = 62.405

The consumer price index of the raincoat by using the todays and the 1983 costs of raincoat is given by option b 151.

Todays cost of raincoat = $79.25

Cost of raincoat in 1983 = $52.48

Calculate the CPI (Consumer Price Index) in 1983,

Use the formula we have,

CPI = (Cost of the raincoat today / Cost of the raincoat in 1983) x 100

Plugging in the values given in the problem, we get,

⇒ CPI = ($79.25 / $52.48) x 100

⇒ CPI = 1.51009 x 100

⇒ CPI = 151.009

Rounding this to the nearest whole number gives a CPI of $151.

Therefore, the best answer to represent the consumer price index of the raincoat is equals to option  (b) 151.

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The magnitude of the net electric field at point P due to the particle is 0 . explanation is given as

let us assume that , The charges of the four particles and the distance are given then on understanding the  concept of electric field  at electrostatics concept. on using the concept of the electric field at any given point, then production of  individual electric field by a charge. and we known the concept of superposition law, on applying the law  we  get the value of the electric field in its direction and this shows the determination of   the net electric field at that point.

The magnitude of the electric field,  

E = q * R

where R = The distance of field at  point from the charge, and q = charge of the individual particle

According to the superposition principle, the electric field at a single point due to more than one charges present ,hence on calculation of net electric field  we get the origin of the coordinate system  which is placed at point P and the y-axis is situated and oriented in the direction of the charge,  (passing through the charge, ). The x-axis which  is perpendicular to the y axis, and thus passes through the identical charges, then the  individual magnitudes of an electric field is due to the charges are demonstrated by using the absolute signs of the charges. Now let us assume that the point charge which  being positive i.e  ( q > 0), we can see that the contributions coming from each charge gets cancel to each other. Therefore the net electric field in the direction of the y-axis is given using equation as  E= 0

hence the net electric field is zero .

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The wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = \(\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h\)

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = \(\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)\)

⇒ \(\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)\)

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = \(\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)\)

⇒ \(\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)\)

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

-1/5

Step-by-step explanation:

We can use the formula [ y2-y1/x2-x1 ] to solve.

3-1/-5-5

2/-10

-2/10

-1/5

Best of Luck!

The points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.

To find the points of inflection, we need to take the second derivative of the function y = (1 + x)/(1 + x²):

y' = (1 - x²)/[(1 + x²)²]
y'' = (-6x)/[(1 + x²)³]

To find the points of inflection, we need to set y'' = 0 and solve for x:

0 = (-6x)/[(1 + x²)³]
0 = -6x

This gives us three possible values for x: x = 0 (where the second derivative changes sign), and x = ±∞ (where the second derivative approaches 0).

To determine which of these points are points of inflection, we need to look at the sign of the second derivative on either side of each point. If the sign changes, then it is a point of inflection. If the sign stays the same, then it is not a point of inflection.

At x = 0, the second derivative changes sign from negative to positive, so this is a point of inflection.

At x = ±∞, the second derivative is always 0, so these are not points of inflection.

Therefore, the points of inflection are x = 0, x = -∞, and x = ∞. These three points lie on the vertical line x = 0.

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The magnitude of the addition of three vectors is equal to 34.405.

Vectors are numbers described by magnitude (r) and direction (θ), in degrees. Vectors in rectangular form are described by expressions of the form:

v = r · cos θ + r · sin θ

Where:

The magnitude of the addition of a given number of vectors can be found by means of Pythagorean theorem:

R = √[(∑ r · cos θ)² + (∑ r · sin θ)²]

R = √[(50 · cos 35° + 65 · cos 180° + 10 · cos 245°)² + (50 · sin 35° + 65 · sin 180° + 10 · sin 245°)²]

R = √[(- 28.265)² + 19.616²]

R = 34.405

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The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Based on the given data, a hypothesis test can be performed to determine if there is sufficient evidence to conclude that the die is loaded. The significance level for this test is 0.05.

In order to conduct the hypothesis test, we can use the chi-squared test for goodness of fit. The null hypothesis (H0) assumes that the die is fair, meaning that each number has an equal probability of occurring. The alternative hypothesis (Ha) suggests that the die is loaded, meaning that the probabilities are not equal.

Using the chi-squared test, we can calculate the test statistic and compare it to the critical value from the chi-squared distribution with 5 degrees of freedom (6-1). If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The chi-squared test will assess the difference between the observed frequencies and the expected frequencies assuming a fair die. If the observed frequencies deviate significantly from the expected frequencies, it would indicate that the die is loaded.

Performing the chi-squared test and comparing the test statistic to the critical value at a significance level of 0.05 will allow us to determine if there is sufficient evidence to conclude that the die is loaded.

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Answer:

The number is 270

Step-by-step explanation:

Let the number be 'x'

3/5 of x = 162

\(\frac{3}{5}*x = 162\\\\x=162*\frac{5}{3}\\\\x=54 * 5\\\\x = 270\)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{270}}}}}\)

Step-by-step explanation:

Let the number be 'x'

\( \sf{ \frac{3}{5 } \: \: of \: x \: = 162}\)

⇒\( \sf{ \frac{3x}{5} = 162}\)

Apply cross product property

⇒\( \sf{3x = 162 \times 5}\)

Multiply the numbers

⇒\( \sf{3x = 810}\)

Divide both sides of the equation by 3

⇒\( \sf{ \frac{3x}{3} = \frac{810}{3} }\)

Calculate

⇒\( \sf{x = 270}\)

Hope I helped!

Best regards!!

Answer:

Triangular prism

Step-by-step explanation:

Answer: Shape

Step-by-step explanation: Aww don't worry I got you here's the answer Triangular prism.

Answer:

\(y=3x-7\)

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

\(m=\frac{y_2-y_1}{x_2-x_1}\) where the points given are \((x_1,y_1)\) and \((x_2,y_2)\)

Points (3,2) and (6,11)

\(=\frac{11-2}{6-3}\\=\frac{9}{3}\\= 3\)

Therefore, the slope of the line is 3. Plug this into \(y=mx+b\):

\(y=3x+b\)

2) Determine the y-intercept (b)

\(y=3x+b\)

Plug in one of the given points and solve for b

\(2=3(3)+b\\2=9+b\)

Subtract 9 from both sides

\(2-9=9+b-9\\-7=b\)

Therefore, the y-intercept of the line is -7. Plug this back into \(y=3x+b\):

\(y=3x-7\)

I hope this helps!

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

2/11

Step-by-step explanation:

Probability is the LIKELIHOOD of an event.

According to the word problem, there are 11 people in total and 2 of them are being selected.

The probability of them being the 2 oldest people is 2 in 11, or 2/11.

The numeric value of the function g(x) at x = -12 is given as follows:

g(-12) = -10.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the defined function or in the defined expression by the value at which we want to find the numeric value.

On the graph of a function, to find the numeric value for a value of x, we have to trace a vertical line at the value of x and verify where the vertical line crosses the function.

On the given graph, a vertical line at x = -12 would cross the function at y = -10, hence the numeric value is given as follows:

g(-12) = -10.

The graph of the function is presented at the end of the answer.

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Step-by-step explanation:

A + 2 ÷ (-24) = -4

A - 1/12 = -4

A = -4 + 1/12

A = -48/12 + 1/12

A = -47/12

A ≈ -3,91

There are  212520  ways by which guests arrange themselves on a four person coach.

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

there are total 23 guests and they arranged themselves in 4 person coach,

so,

n = 23 and r = 4

npr = n!/(n-r)!

= 23!/(23-4)!

= 23!/19!

= 23x 22 x 21 x 20x 19!/19!

now cancel the factorial 19 from numerator as well as denominator

=  23x 22 x 21 x 20

= 212520

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Given:

A figure of a triangle.

To find:

The measure of angle A.

Solution:

Label the points in the figure as shown below.

In the below figure,

\(\angle ACB\cong \angle DCE\)            (Vertically opposite angles)

\(m\angle ACB=m\angle DCE\)              (Congregant angles)

\(m\angle ACB=8x+4\)

Using exterior angle theorem in triangle ABC, we get

\(m\angle A+m\angle C=\text{Exterior }m\angle B\)

\(m\angle BAC+m\angle ACB=130^\circ\)

\((3x-6)+(8x+4)=130^\circ\)

\(11x-2=130^\circ\)

Isolate the variable term x.

\(11x=130^\circ+2\)

\(11x=132^\circ\)

\(x=\dfrac{132^\circ}{11}\)

\(x=12^\circ\)

Now, the measure of angle A is:

\(m\angle A=3x-6\)

\(m\angle A=3(12^\circ)-6\)

\(m\angle A=36^\circ-6\)

\(m\angle A=30^\circ\)

Therefore, the correct option is B.

The correct answer are as follows

a) True, b) False, c) False, d) False, e) False

(a) True. The standard deviation is always a non-negative value since it is a measure of the spread or variability of the data set.
(b) False. Since A and B are disjoint, they have no overlapping outcomes, which means P(A AND B) = 0.
(c) False. Although the mean and median are often close in a normal distribution, they are not always equal. The median is the middle value of the distribution, while the mean is the average of all values.
(d) False. A 95% confidence interval is narrower than a 98% confidence interval of the same parameter since it requires a higher level of confidence to have a wider interval.
(e) False. If the value of the test statistic is 1.5 and P(T<1.5)=0.98, then the p-value is 0.02. Since the p-value is less than the level of significance of 0.05, we reject the null hypothesis.
(a) True. The standard deviation of a data set cannot be negative because it is a measure of dispersion and is calculated as the square root of the variance, which is always non-negative.

(b) False. If A and B are disjoint, then P(A AND B) = 0, since disjoint events cannot occur simultaneously.

(c) True. For a normal distribution, the mean is always equal to the median, indicating a symmetrical distribution.

(d) False. A 95% confidence interval is narrower than a 98% confidence interval of the same parameter because a higher confidence level requires a wider interval to capture the true value with greater certainty.

(e) True. In a two-tailed test, if the test statistic follows a Student's t-distribution with P(T<1.5)=0.98, this means that P(T>1.5)=0.02. For a two-tailed test at a 0.05 level of significance, the rejection regions are in both tails, with 0.025 in each tail. Since P(T>1.5)=0.02 < 0.025, we fail to reject the null hypothesis.

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Answer:

100

Step-by-step explanation:

Hello,

We are looking for the surrounding perfect squares.

\(\sqrt{8000}=89.44272...\)

so

\(7921=89^2< 8000<90^2=8100\)

So we need 100 more soldiers to form a perfect square.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

3rd one im pretty sure

Step-by-step explanation:

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer: 104.65%

Step-by-step explanation: 45/43=1.0465 so you just move the decimal to the right 2 places to make it a percent. It’s over 100% because 45 is higher than the total of 43.

Answer:

0.101

Step-by-step explanation:

\(speed = \frac{distance}{time} \)

We have speed, and we have distance. So let's rearrange to get time:

\(time = \frac{distance}{speed} \)

Let's plug in our numbers (make sure to times distance by 1000 to convert to metres):

\(time = \frac{30425000}{3.0 \times {10}^{8} } \)

Which leaves us with:

\(time = \frac{1217}{2 ^ {5} \cdot 3 \cdot 5 ^ {3}} \approx 0.101416667\)